Sen. Lindsey Graham’s approval is slipping in South Carolina, two new polls show, but the challengers for his Senate seat still aren’t offering him a significant threat.

Graham’s approval in his home state has dropped nearly 30 points among conservatives in a new Winthrop University poll. Among Republicans and GOP leaners, 45.2 percent approve of the job Graham is doing, down from 71.6 percent in February. His approval among all registered voters stands at 37.4 percent, with 48.5 percent disapproving.

Those numbers are similar to a new poll out Wednesday from conservative firm Harper Polling, which found likely voters had a 44 percent to 37 percent unfavorable view of the Republican senator.

Nevertheless, Graham is soundly beating his declared Republican primary and Democratic challengers in the Harper poll. Fifty-one percent of likely GOP primary voters favored Graham, compared to 15 percent for his next closest challenger, state Sen. Lee Bright. Citadel graduate Nancy Mace and the other candidates each got 4 percent of the primary vote.

Graham also led among likely voters in the general election, leading Democrat Jay Stamper 47 percent to 30 percent.

Graham’s Republican challengers have criticized him for his willingness to work with the president on certain issues, including on Syria. He is up for reelection for what would be his third term in 2014.

Winthrop surveyed 887 South Carolina adults from Oct. 19 to 27 for its poll, which has an error margin of plus or minus 3.3 percentage points. Harper surveyed 676 likely voters from Oct. 27 to 28 for its poll, which has a margin of error of plus or minus 3.77 percentage points. For the GOP primary question, 379 likely GOP primary voters were polled with an error margin of plus or minus 5.03 percentage points.